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Woven Nano-Structure of Carbon Nanotubes

We have studied the above woven nano-structure of carbon nanotubes as one of potential designs for ballistic-resistance materials via the atomic-scale finite element method (AFEM). Our study shows that this structure is insensitive to structure defects. More details can be found in our paper.

Thanks for your interest in our work. From my understanding, in the traditional FEM, the space of interest is firstly divided into many non-overlapping subspaces, so-called elements, and the energy is then divided correspondingly. The energy in each element can be determined with the node positions of this element only. This is just the local feature of the traditional FEM. Therefore, the traditional FEM is only accurate for systems with the energy distributed locally, such as the bond energy in terms of pair potential.

However, for systems with multi-body potentials, it is not easy to accurately assign the energy into subspaces or non-overlapping elements. Therefore, we do not divide the energy in AFEM, and directly compute the first and second order derivatives of the total energy with respect to one specific node position. This node and its neighboring nodes that are needed to compute these derivatives form one AFEM element. With this strategy, we can obtain global stiffness force matrixes without any approximation (e.g. shape function), which ensure the AFEM is as accurate as other standard atomistic simulation methods. Moreover, by taking advantage of mature FEM numerical techniques, AFEM is much faster than existing molecular mechanics methods.

Sure, AFEM can be used in dynamics simulation. Since we already know how to compute the stiffness matrix and the mass matrix is easily abtained, the AFEM dynamics simulation is the similar to traditional FEM.

I also read the paper by Liu, et al. about the atomistic finite element modeling. The main difference between conventional FEM and atomstic finite element modeling, as far as I understand, is the empirical potential field. For instance, in Liu's paper, they used the empirical potential, provided by Brenner or others, for carbon atoms. For potential field, they considered the short-range interaction for CNT such that, for a given atom i, the neighborhood atoms near atom i are taken into account for finding stiffness matrix and force vector based on empirical potential.

The simple mechanics model is working very well for not only nanomaterials (e.g. CNT) but also biomolecules (e.g. proteins), since the dynamics of nanomaterials and/or biomolecules are well described by stiffness matrix and force vector on the basis of empirical potential field (e.g. Brenner's potential for CNT; Tirion's potential for proteins; CHARMM for proteins, etc.). For instance, the stiffness matrix based on Tirion's model (harmonic potential field for short-rang interaction) is sufficient to represent the low-frequency normal mode dynamics of proteins (for details, click here).